{
  "abstract": "The exact local exchange-energy density, obtained from the Slater potential of the Hartree-Fock exchange hole, is a central ingredient of Becke's B05 and B13 functionals and of many other local hybrids. It is usually evaluated in a Gaussian basis, so the local quantity retains a pointwise basis-set incompleteness error. We describe here a basis-set-free numerical code that solves the Kohn-Sham problem on real-space grids for atoms, diatomics, and polyatomics, and returns the exact local exchange-energy density together with the density, its derivatives, the kinetic-energy density, and the reverse Becke-Roussel hole quantities. Reconstructed from the published record of Becke's non-public NUMOL code, AXEL reproduces numerical atomic references through krypton, scalar-relativistic uranium orbital energies, and Becke's diatomic spectroscopic constants. We then extend the original local-density numerical framework to generalized-gradient and hybrid functionals. Comparisons with the independent adaptive-multiwavelet code MRChem give sub-millihartree agreement for Hartree-Fock and PBE0. The same calculations agree with large Gaussian-basis references to a similar level of accuracy. Atom-centred eXact Electronic Limit (AXEL) is intended as both a basis-set-free numerical reference and a platform for exchange-hole-based density-functional development.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2610.19031",
  "author_total": 1,
  "authors": [
    {
      "name": "Alastair J. A. Price"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/6nmjdh6w2qjmf.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2610.19031",
  "fulltext_url": null,
  "id": "6nmjdh6w2qjmf",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2610.19031",
  "language": null,
  "licence": "CC-BY-4.0",
  "licence_label": "CC BY 4.0",
  "licence_source": "article",
  "licence_url": "http://creativecommons.org/licenses/by/4.0/",
  "metadata_licence": "CC0-1.0",
  "native_subjects": [
    [
      "arxiv",
      "physics.chem-ph"
    ],
    [
      "openalex",
      "3107|Advanced Chemical Physics Studies"
    ]
  ],
  "openalex": "W7222123928",
  "pdf_url": "https://arxiv.org/pdf/2610.19031",
  "pmcid": null,
  "pmid": null,
  "published": "2026-10-13",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/6nmjdh6w2qjmf.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:29:31Z",
      "native_id": "2610.19031",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2610.19031"
    }
  ],
  "subjects": [
    {
      "field": "chemistry",
      "origin": "arxiv:physics.chem-ph",
      "subfield": "physical"
    }
  ],
  "title": "A basis-set-free reference for the exact exchange-energy density and functional development",
  "title_text": "A basis-set-free reference for the exact exchange-energy density and functional development",
  "type": "preprint",
  "updated_at": "2026-10-30T12:29:31Z",
  "url": "https://research.draconitic.com/paper/6nmjdh6w2qjmf",
  "venue": "arXiv",
  "versions": []
}